High-Dimensional Causal Discovery Under non-Gaussianity

TL;DR

This paper introduces a high-dimensional causal discovery algorithm for linear structural equation models with non-Gaussian errors, capable of accurately identifying causal graphs even when the number of variables exceeds observations, under sparsity and log-concavity assumptions.

Contribution

It presents a novel algorithm for consistent causal graph estimation in high-dimensional non-Gaussian linear models, extending previous methods to larger variable sets with sparsity constraints.

Findings

Algorithm achieves consistent graph estimation in high-dimensional settings.

Theoretical guarantees are provided under log-concave error distributions.

Method outperforms existing approaches in scenarios with many variables.

Abstract

We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific error term and the other observed variables $Y_u$ with $\sigma(u) < \sigma (v)$. The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has been previously shown that when the variable specific error terms are non-Gaussian, the exact causal graph, as opposed to a Markov equivalence class, can be consistently estimated from observational data. We propose an algorithm that yields consistent estimates of the graph also in high-dimensional settings in which the number of variables may grow at a faster rate than the number of observations, but in which the underlying causal structure features suitable sparsity; specifically, the maximum in-degree of the graph is controlled. Our theoretical analysis is couched in the setting of log-concave error distributions.